


Standardization of Some of the 
Common Tests Used in Deter- 
mining the Acuteness of 
Vision of School 
Children 



BY 

J. M. McCALLIE 

TRENTON, N. J. 



A Thesis Submitted to the Faculty of the 

Graduate School of the University of 

Pennsylvania in Partial Fulfilment 

of the Requirements for the 

Degree of Doctor of 

Philosophy 



STANDARDIZATION OF SOME OF THE COMMON 

TESTS USED IN DETERMINING THE 

ACUTENESS OF VISION OF SCHOOL 

CHILDREN 






J. M: McCALLIE 



TRENTON, N. J. 



A Thesis Submitted to the Faculty of the Graduate School 
of the University of Pennsylvania in Partial Fulfil- 
ment of the Requirements for the Degree of 
Doctor of Philosophy 

June, 1912. 



L"B 3 4 5" J 
.M3 



19/8 



STANDARDIZATION OF SOME OF THE COMMON 

TESTS USED IN DETERMINING THE 

ACUTENESS OF VISION OF SCHOOL 

CHILDREN 

Most, if not all of the tests, both letters and characters, 
used for testing the acuteness of school children are based, 
in theory, at least, upon the Snellen test letters. 

Since the Snellen letters will be referred to often, a brief 
account of their origin and structure is here given : 

In 1862, Dr. Herman Snellen, professor of ophthalmolgy in the Uni- 
versity of Utrect, Holland, and director of the Netherlands Institute for 
Diseases of the Eyes, published an improved series of test types for 
measuring the acuity of vision.* The principle which guided him in the 
constmction of these test letters is based upon the fact that the normal 
eye can just discern objects that subtend a one minute angle, the vertex 
of the angle being* the point where the rays of light cross before falling 
on the retina. 

In order that a letter may be recognized each one its elements must 
be discernible, hence, each of these elements must have a diameter equal 
to the tangent of an angle of at least one minute. In constructing uni- 
form letters in conformity with this principle, Snellen found that each 
letter must have at least one diameter equal to the tangent of a five- 
minute angle. Each letter is therefore made in a square which is sub- 
divided into twenty-five equal squares, each small square being equal in 
diameter to the tangent of a one-minute angle. Since the tangent of a 
five-minute angle is equal to 0.001454, to obtain the longest diameter of 
a letter to be seen at a given distance, Snellen multiplied the length of 
the tangent of five minutes by the distance, in centimeters, of the letter 
from the nodal point of the eye; thus, at a distance of one-hundred cen- 
timeters the height of the letters should be 0.1454 centimeter, and each 
stroke of the letter should be at least one-fifth of this, or 0.0291 in 
length. 

Before beginning the work a large number of test cards 
were collected from different dealers. On some of these 
were lines of letters of different sizes, on others, lines of 
pictures or characters of different sizes. Under each one 
of these lines of different sized letters, pictures, or charac- 
ters, was printed the distance at which they were supposed 
to be seen by the normal eye. An examination of this col- 



*Snellen, H. Optotypi ad visum determinandum secundum formu- 



d_ 
D 
scharfe.) Berlin, H. Peters. 1904. 



larum y — Ed. XVII. (Probebuchstaben zur Bestimmung der Seh- 

D 



lection of material soon disclosed the fact that there was no 
uniformity either in the size, style, or structure of the let- 
ters or characters or pictures, gotten out by different 
houses, which were supposed to be seen at the same distance 
by the normal eye. Not only was there a lack of uniform- 
ity, but, not on a single card, could there be found a set of 
letters or characters or pictures whose proportions were in 
accordance with the Snellen measurements. And, not only 
were these out of proportion, according to Snellen, but they 
were not of the right size to be seen at the different dis- 
tances. The letters and characters intended to be read at 
the shorter distances were generally printed so poorly as 
to make them useless as tests. Add to these faults the facts, 
that these letters and characters were printed in black on 
several shades of white or cream colored cardboard or 
different shades of white letters on black cards, and, that 
the finish of the cardboard varied from a glossy white or 
black to a lustureless white or black, and it can readily be 
seen that there could be no uniformity of results, to say 
nothing of accuracy or the possibility of selecting any one 
of these measures for a standard. It was evident, there- 
fore, that if my work was to have any value, new letters 
must be made. This was done by most accurately drawing 
the letters according to the Snellen dimensions from which 
new and accurate type were made, and, from which, the 
letters used in these tests were printed, except the tests 
made in comparing the relative visibility of the "illiterate 
E," with the 16 ft. letters. 

The picture' tests were discarded because they were not 
and could not be constructed according to the Snellen 
measurements, consequently the results obtained could not 
be compared with results obtained by tests made with the 
Snellen letters. 

The tests made were divided into two parts. The first 
had to do with the visibility of the "illiterate E," supposed 
to be seen by the normal eye at no greater distance than 
16 ft., as compared with the visibility of the Snellen letters 
constructed to be seen by the normal eye at no greater dis- 
tance than 16 ft. 

The second part had to do with determining whether 
tests made by the Snellen 12 ft., or 16 ft. letters, or a dot, 



supposed to be seen at 20 ft., are not as accurate as tests 
made with letters to be seen 50 ft., 40 ft., 30 ft., or 20 ft. 

The following is a detailed description of the method 
and results obtained by comparing the visibility of the 
"illiterate E" with the Snellen test letters of the same di- 
mensions : 

As stated above, types for the 16 ft. "illiterate E" and 
the 16 ft. letters were not made anew. This was not neces- 
sary because a copy of Snellen's classic work on test types 
was found which contained the "illiterate E" and the let- 
ters of the desired size. The letters taken from this book 
were O, L, N, Z, B, D, T, and E, and the "illiterate E" 
turned up, down, right, and left, (see Pig. 1) all of which 
were supposed to be visible to the normal eye at 16 ft. 
These were printed on white unglazed paper about the 
thickness of ordinary book paper. 

The 16 ft. letters and the 16 ft. "illiterate E," were 
selected of one and the same size to enable comparison of 
results to be made more readily and because the size of the 
rooms in which the tests were made would not admit of 
using larger letters. 

Each one of these letters and "illiterate E's," were 
carefully cut out, and pasted on white unglazed cards, 
three and one-half by six inches, one and one-half inch 
from the top of the card and equally distant from the sides, 
one letter or one " illiterate E" on a single card. On the 
back of each card was written the same letter or ' ' illiterate 
E" that appeared on the front. This was for the purpose 
of enabling the operator to know the letter or to tell which 
way the "illiterate E," was turned, when presented to the 
subject. 

By having the letters on separate cards, so that only 
one letter was in view at a time, the operator could be 
sure that the pupil's reply was a judgment on that letter 
and not on some other letter, as often happens when several 
letters are shown at one time. This arrangement, also, 
made it possible to vary the order of presentation, and, so 
prevent the letters from being memorized. The operator 
by this device was left free to give his entire attention to 
the efforts put forth by the children in reading the letters. 
By holding the cards in his hands, the operator was enabled 



6 

to utilize the best light in the room more easily than if he 
had used a large card hung on the wall, as is usually done 
in such tests. 

The best position for exhibiting the letters, so far as 
light was concerned, was selected, and, beginning with this 
position, short chalk marks were made on the floor every 
two feet the entire length of the room, the first mark being' 
two feet away from the position selected for best light, the 
second four, and so on. 

Everything being ready, the pupils were called one at a 
time and told to stand with their toes to line twenty, with a 
card held over one eye. Two or three letters were pre- 
sented. If the pupil could not read them, he was asked to 
step up two feet and try again. If he failed again, he was 
asked to step up two more feet and try again. If he failed 
at this distance — sixteen feet — he was asked to step up 
one foot at a time, after each succeeding failure, until he 
was able to read at least five consecutive letters correctly. 
The letters were not exposed to view longer than two sec- 
onds. If the correct names of five consecutive letters could 
not be read in the time limit, the result was counted a fail- 
ure, until a distance was found where the letters could be 
read. If the subject could read all the letters correctly at 
sixteen feet, this fact was indicated by placing the fraction 
16/16 opposite his name on the record sheet. If he could 
read the letters only at six feet, this fact was indicated by 
the fraction 6/16. If the letters could be read at twenty- 
four feet, this fact was represented by the fraction 24/16, 
etc. 

Having determined the greatest distance at which one 
eye could read the letters, the same process was repeated 
with the other eye. Immediately after each pupil was test- 
ed with the alphabet cards he was tested with the ' ' illiterate 
E," cards, by the same general method, except that instead 
of naming the character the pupil was required to point in 
the direction, up, down, right, or left, thus indicating the 
direction of the opening of the E. In this case, as with the 
letters, a single error was taken to indicate that the pupil's 
vision was not sufficiently acute to read the characters at 
that particular distance, and he was required to move to- 
ward the cards until he reached the point at which at least 



five consecutive characters could be read correctly within 
the allotted time of not more than two seconds each. 

In doing this work the tests with the "illiterate E," al- 
ways followed the test with the letters, so, if fatigue played 
any part in the tests it would show itself in the results ob- 
tained with the "illiterate E." 

Before beginning the test each day, the operator tested 
his own vision to see whether the light was satisfactory. 
Tests were made only on days when the light was good. No 
work was done on cloudy or dark days. These tests were 
carried on in the different class-rooms, and, so far as each 
pupil was concerned the test with the "illiterate E," and 
the letters were made under exactly the same conditions. 

470 children took the tests during the months of April 
and May. 

The results of these tests are presented in the table I. 
This shows the number of eyes tested in grades I to VIII, 
with the greatest distances at which the alphabet and illit- 
erate characters could be distinguished, Four hundred and 
seventy pupils, or 940 eyes, were tested. These pupils were 
distributed throughout the grades as follows : 72 in the 
first grade, 54 in the second, 39 in the third, 28 in the fourth, 
41 in the fifth, 29 in the sixth, 130 in the seventh and 77 in 
the eighth. The 344 pupils in grades III to VIII, inclusive, 
were tested with both the alphabet and illiterate characters. 
In columns headed Totals II to VIII, may be found the fig- 
ures affording the most ready comparison of the results 
with the alphabet characters, and illiterate cards. Thus, 
with the alphabet characters, the largest number of eyes, 
148, distinguished the letters at fourteen feet; the next 
largest 128, at sixteen feet, and the next largest 114, at 
twelve feet. Of these 688 eyes tested, 390, or 56.7 per cent., 
distinguished the letters at from twelve to sixteen feet. 
With the illiterate cards, however, these same eyes dis- 
tinguished the "illiterate E" at a much greater distance, 
in fact, 94 pupils saw the "illiterate E," at twenty- two feet. 
This was the largest number seeing this character at any 
distance, and the next largest number, 92, saw it at twenty- 
four feet. The next largest number, 86, saw it at twenty 
feet. The results of this comparative test with two 
characters are graphically exhibited in Graph I. Curve I 



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represents the results of the alphabet test and Curve II 
represents the results of the ' ' illiterate E ' ' test. 

The pupils of the first and second grades, 126 in all, 
were tested with the "illiterate E" only, because they did 
not all know the letters of the alphabet. Curve III repre- 
sents the results obtained by testing these 252 eyes with the 
illiterate cards. Curve IV combines in a single curve the 
results of the illiterate test with the 470 pupils in all grades. 




Z 4 6 8 /O fZ J4 /6 /8 ZO ZZ Z4 & 23 30 32 34 36 36 40 4244 
Geaph 1. 

The straight line a-b, running perpendicularly through 
the curves, is the line of assumed normal vision for all of 
the tests. If this were correct, then all of the eyes repre- 
sented by the portion of the curves to the left of this line 
are subnormal, and all eyes represented by that portion of 
the curve to the right of the perpendicular are above nor- 
mal in acuteness. 

From these curves we deduce the following results : 



Curve I (alphabet test) . . 
Curve III ("illiterate E") 



Eyes Normal 

128 or 18.6% 

27 or 3.9% 



Eyes Subnormal 

453 or 65.8% 

56 or 8.1% 



10 

Eyes Above Normal 

Curve I (alphabet test) 107 or 15.5% 

Curve III ("illiterate E") 566 or 82.2% 

It is evident at a glance, that something is wrong, either 
with the letters used or with the "illiterate E," since the 
results were obtained under exactly the same conditions. 
It is not possible for both results to be correct, because with 
the "illiterate E," 8.1 per cent, of the pupils tested were 
subnormal and 82.2 per cent, were above normal ; whereas, 
with the alphabet test, 65.8 per cent, of the same pupils 
were found to be subnormal and only 15.5 per cent, above 
normal. The fact that only 3.9 per cent, of the pupils, ac- 
cording to the illiterate test, had normal vision, and only 
8.1 per cent, were subnormal, would warrant the suspicion 
that something was wrong with the "illiterate E," as a 
reliable measure for acuteness of vision. A close analysis 
of this character will prove that the suspicion is well found- 
ed. The structure of the "E" is shown at the right of 
Graph I. 

A pupil being tested with this character has only to de- 
termine in which one of the four directions up, down, right, 
or left, the opening of the character is directed, and this 
opening can always be pointed out by observing that this 
side of the E is always the lightest. Each of these char- 
acters, as before stated, is constructed in a square which is 
subdivided into twenty-five squares. The normal eye is 
supposed to be able to discern one of these small squares 
at the same distance at which the E, turned in different 
directions can be recognized. It will be observed that there 
are three of these small squares lying together unfilled on 
the open side of this character. Four of these small 
squares, arranged in the form of a square has twice the 
diameter of the small square and should be discerned at 
twice the distance or 32 feet. It would, therefore, be rea- 
sonable to suppose that these three unfilled squares lying- 
one above the other should be seen at about three-quarters 
of that distance, or twenty-four feet. As a matter of fact, 
this is exactly the distance at which they were discerned by 
the largest number of the pupils of all grades. 

This comparative test proves conclusively that sixteen 
feet is not the distance at which the normal eye can just 



11 

discern the "illiterate E." In fact, twenty-nine eyes were 
found, exhibiting normal vision with the alphabet test, 
that could interpret these characters at twice sixteen feet. 
Many could read them farther than thirty-two feet, in fact, 
two could do this at forty-four feet and one could make 
them out at fifty feet. 

It is evident then, that if this character is to be used 
for testing the acuteness of vision, a new distance, at which 
the normal eye can just see it, must be determined or the 
size of the characters must be changed. Either or both of 
these changes can easily be deduced from the results ob- 
tained by these tests. 

Assuming that sixteen feet is the distance at which the 
sixteen foot letter can just be made out, by the average 
normal eye, then, the same relative variation from this 
normal sixteen foot distance, would be found to obtain in 
any sized letter or characters used in a series of tests. For 
example, if a series of tests with the sixteen foot letter, 
should show that the eyes tested could see the letters at an 
average distance of only twelve feet, or one-fourth less than 
normal distance, and, if another series of tests, made on 
the same eyes with another set of letters of any given uni- 
form size and structure, should show that they could be 
seen at twenty-four feet, then the distance, twenty-four 
feet, should vary as much from the normal distance, at 
which such letters should be seen, as twelve feet varies from 
sixteen feet, the normal distance at which the sixteen foot 
letters should be seen. It is evident that the distance 
twelve feet is one-fourth less than the normal distance six- 
teen feet, and, since the same relation must exist in the 
series of tests which showed that the average distance at 
which letters or characters could be seen was twenty-four 
feet, then this distance, twenty-four feet is one fourth less 
than, or three-fourths of the distance at which the normal 
eye can see these letters or characters. If twenty-four feet 
is three-fourths of this normal distance, then the distance 
at which the normal eye should see these letters or char- 
acters is, 4/3 of 24 ft., or 32 ft. 

In the series of tests described above it was found that 
the average distance at which the 688 eyes could just see the 
sixteen foot letters was 13.7 ft., and the average distance 
at which the same 688 eyes could see the "illiterate E," at 



12 

the same time was 23.2 ft. The distance at which the nor- 
mal eye can see the sixteen foot letters is 16/13.7 of 
the average distance at which the letters were seen. Since 
the same relations must exist between the normal distance 
at which the ''illiterate E," can be seen and the average 
distance at which it was seen, we find this normal distance 
by taking 16/13.7 of 23.2/1 ft., the distance at which the 
"illiterate E" could be seen. This gives 26.4 ft., which is 
the distance at which the normal eye can see the ' ' illiterate 
E" used in these tests, instead of sixteen feet as was given 
by Snellen. 

If it is desired to change the size of the "illiterate E," 
so that it can just be read at sixteen feet, instead of chang- 
ing the distance at which it can just be seen, this can be 
readily done by making it just 16/26.4 of the size used in 
these tests. As these tests clearly show, one or the other 
of these changes should be made if the "illiterate E" is to 
be used as a test. 

The second part of the problem has as its object, as 
already stated, the determination of whether the Snellen 
12 ft., or a 16 ft. letter, or a black dot whose diameter is 
one-fifth the greatest diameter of a Snellen 20 ft. letter, 
might not be as reliable tests for acuteness of vision as the 
tests made with the Snellen 20 ft., 30 ft., 40 ft., or 50 ft. 
letters. 

The vision of 200 pupils in the fifth, sixth, seventh, and 
eighth grades of a public school were tested in arriving at 
a solution of the second part of the problem. 

The following is a description of the method used in 
making these comparative tests : 

The tests were made in a room about 90 ft. long, near 
one end of which was a window so situated as to give an 
excellent light, in which to exhibit the letters in making the 
tests. A chalk mark was placed on the floor at the point 
where the light was best. Measuring from this line, a chalk 
mark was placed on the floor every two feet for the entire 
remaining length of the room which was 84 ft. These marks 
were numbered as follows : the first line, made on the floor 
at the point of best light, was marked ; the next line, two 
feet away, 2 ; the next line, 4 ; the next, 6, etc., up to 84. This 
gave a clear range of vision of 84 feet. 



13 

It was decided beforehand that the letters and dots 
should be exhibited one at a time and that each should be 
exposed to view not longer than two seconds. 

As stated above, it was not possible to find test cards 
printed in clear type of the right dimensions, and, it was 
also impossible to use these test cards for testing pupils 
with the different sized letters without some of the letters 
being memorized, thus thwarting the purpose of the tests. 
To overcome these difficulties, it was found not only neces- 
sary to have new types constructed with the correct dimen- 
sions, according to the Snellen measurements, but to de- 
vise entirely new vision test cards. These cards serve the 
double purpose of allowing only one letter to be seen at a 
time, and rendering it impossible for anyone to remember 
the order of the letters, and, beside, the tests can be made 
with much greater ease, accuracy, and rapidity than can be 
done with the ordinary test cards. 

A set of these new test cards consists of twelve square 
cards about 5 in. x 5 in., on which are printed forty-eight 
letters of four sizes, one letter of each size on each card, no 
two cards having the same letters on them. The different 
sized letters can be seen by the normal eye at 20 ft., 30 ft., 
40 ft., and 50 ft., respectively. These four letters, on each 
card, are placed so 'that one appears one-half inch from each 
margin and equally distant from the sides. And they are 
printed in such a way that only the letter at the top of the 
card is in a position to be read when the card is held in an 
upright position. 

A reduced copy of one of these cards is shown in Fig. 2. 

The tests are made with these cards exactly as tests 
are made with the ordinary test cards, except that the oper- 
ator holds the cards in his hand and exhibits one letter at 
a time, by taking the cards one at a time, from the back of 
the pack and placing them in front. Any one of the four 
sized letters may be used by simply giving the cards a 
quarter or a half turn in the hands. Any possibility of re- 
membering the order of the letters may be prevented by 
now and then shuffling the cards. This makes it possible to 
test pupils in their own rooms and in the presence of all 
the pupils if desired, and obtain trustworthy results. 

In making tests with the black dots which were sup- 
posed to be seen at 20 ft., the first thing to consider was the 



14 



T 



o 



w 




Figure 2. Showing the four sizes of letters and their 
arrangement on one of the twelve cards used in these tests. 
The smallest of these letters can be seen by the normal eye 
at 20 ft. ; the next larger, 30 ft. ; the next larger, 40 ft. ; and 
the largest, 50 ft. 



15 

size of the dot. According to the rule laid down by Snellen, 
the normal eye can just discern an object whose largest di- 
ameter is one-fifth of that of a letter which can just be dis- 
cerned at the same distance. A letter to be just discerned 
at 20 ft. should be 0.349 inches in height or in the largest 
diameter, so, the size of the dot to be seen at 20 ft., should 
be one-fifth of 0.349 inches or 0.0695 inches in diameter. 
Accordingly, a dot as nearly this dimension as possible was 
carefully constructed. 

To enable one to make tests with the dot rapidly and to 
add interest to the work, another set of test cards was de- 
vised embodying the following, somewhat novel features, 
as shown in Fig. 3, Fig. 4, Fig. 5, and Fig. 6. 

It takes ten of these cards to make a set. The dot in the 
ring is the object to be seen. There are three cards with 
the dot in the boy's ring; three with the dot in the girl's 
ring; three' with the dot in the bear's ring; and one with no 
dot in either ring. All of the dots are identical in size. 

The boy, girl, and bear are supposed to be playing ball, 
and each player is supposed to be trying to catch the ball 
in his racket. The dot is the ball and the rings are rackets. 

The tests were made in this way : The pupil to be tested 
was placed at the distance where the normal eye can just 
see the dot. The operator shuffled the cards and then held 
them up face toward the pupil. As the cards were taken 
from the back of the pack and placed in front, the pupil 
was required to tell which had the ball, by saying "boy," 
"bear," etc., or, if he did not see the dot at all, by saying 
"nobody has it." This method, was found to have the 
great advantage of being easily understood by children and 
interesting to them. Even pupils in the kindergarten may 
be tested with these cards used as a game. 

Having determined the kind of tests to be used and 
selected the position for the best light in which to exhibit 
the tests, and having marked off the floor as in making the 
tests with the "illiterate E" and the 16 ft. letters, and hav- 
ing swung a pendulum to beat seconds, the testing pro- 
ceeded as follows : 

An assistant took a set of the alphabet test cards and 
holding them in front of him in his two hands, took a card 
from the back and put it in front every two seconds, accord- 



16 




Figure 3. Dot test for acuteness of vision showing one 
position of the dot. 



17 




Figure 4. Dot test for acuteness of vision showing- 
absence of dot. 



18 




Figure 5. Dot test for acnteness of vision showing 
a second position of the dot. 



19 




Figure 6. Dot test for acuteness of vision showing a 
third position of the dot. 



20 

ing to the beat of the pendulum. The cards were required to 
be held in the proper position to receive the best light. 

The operator then, instructing the assistant to show 
the fifty foot letters, placed the subject with his toes to 
some mark beyond the fifty foot mark, say 60 ft., and re- 
quired him, with both eyes open, to name the letters as they 
were presented by the assistant. If he could not correctly 
name five letters consecutively, he was instructed to move 
up two feet and try again. If he still failed to name cor- 
rectly, the five letters consecutively, he was required to 
move up two feet more and try again, and so on, until a 
position was found where he could read the required num- 
ber of letters consecutively. If it was found that the sub- 
ject could read with ease all the letters while on the 60 ft. 
line, then he was required to move back two or more feet at 
a time until a position was found, where, at least five con- 
secutive letters could just be read. When it was evident 
to the operator that mistakes were due to inattention or 
other causes than inability to see, another trial was allowed. 

After the distance at which the 50 ft. letters could just 
be seen was found, the distances at which the 30 ft. and 20 
ft. letters could just be seen was determined in the same 
manner. 

The determination, at which the 20 ft. dot could just be 
seen followed the test with the 20 ft. letters, and was car- 
ried out in this way: The operator held in his hands the 
set of ten cards, described above, and presented them in the 
same manner as in making tests with the cards containing 
the alphabet. However, as none of the pupils understood 
what they were to do in this test, the method was explained 
to each pupil or several at a time by showing them the cards 
by saying, "Pupils the boy, girl, and bear are playing a 
game of ball. The dot is the ball. As each new card is pre- 
sented the dot changes position from the ring or racket of 
any one of the players to either of the other two players, or 
the one having the ball may keep it through one or more 
changes. As in a real game, the ball may be lost, so, in 
this game, and the lost ball is indicated by a card being pre- 
sented on which no ring contains a dot. Now, you are to 
be the umpire of the game and your duty will be to tell who 
has the ball as the cards are changed. ' ' A few cards were 
then presented and the pupils were required to tell who had 



21 

the ball. When the game was understood, the pupil to be 
tested was told to stand at the 16 ft. or 18 ft. line and try 
seeing the dot a few times. After he saw it at this distance 
he was required to move back two or more feet at a time 
and try again, and so on, until a distance was found, at 
which, the dots or blanks on five consecutive cards could 
just be made out. This distance was recorded as the dis- 
tance at which the dot could just be seen. 

When through testing with the 20 ft. dot, the subject 
was then tested with the 16 ft. letter and then with the 12 ft. 
letter, exactly in the same manner as the tests were made 
with the 50 ft., 40 ft., 30 ft., and 20 ft., letters. In passing 
pupils through each of these seven tests consecutively, it 
was found that results were often modified by the eyes be- 
coming fatigued. When this was found to be the case, the 
subject was allowed to rest for a short while. 

Realizing that fatigue might modify results if each one 
of the 200 pupils were tested first with the 50 ft. letter, then 
the 40 ft. and so on, down to the 12 ft. letter, every other 
pupil began his test with the 12 ft. letter, then took the 16 
ft. letter, then the 20 ft. letter and so on, up to the 50 ft. 
letter. By this method it can readily be seen that, what- 
ever effects fatigue might produce, this effect would be 
equally distributed, and consequently, it would be non- 
effective, so far as the purpose of these tests is concerned. 

These tests were conducted for each pupil in the same 
room, and with the same kind of daylight as far as possi- 
ble. Care was taken not to make tests on cloudy or dark 
days. 

Since the purpose of these tests was to find out how far 
each pupil could see the different sized letters and the dot, 
or how acute vision was, the pupils were allowed to use 
both eyes at once. This was done because looking with the 
two eyes is the normal way of seeing things, consequently, 
it is believed that the results obtained more nearly repre- 
sent the true acuteness of vision of the pupils tested, than 
if each eye had been tested separately. Pupils wearing 
glasses were tested with their glasses on. 

Tables 2, 3, 4, 5, 6, 7 and 8, pages 23-27, show in detail 
one phase of the results of these tests. 



22 

Column (A) gives the number of pupils who saw the dot 
or letters at the same greatest distance. 

Column (B) hsows the greatest distances at which the 
different groups of pupils in column (A) could see the dot 
or letter. 

Column (C) gives the combined distances at which the 
groups of pupils in (A) could see the dot or different sized 
letters. 

In each of these tables the sum of column (A) equals 
200, the total number of pupils tested. The sum of column 
(C) in each table equals the total combined distance at 
which all of the 200 pupils could see the letters or dot 
used in the test. Therefore, it is evident that if these total 
combined distances in each table were divided by 200, the 
number of pupils tested, the result will be the average 
greatest distance at which these pupils could see the letters 
or dots with which they were being tested. The perform- 
ance of this operation gives the following results : 

The total combined distance at which the 200 pupils saw 
the 50 ft. letters is 10,894 ft. This divided by 200 gives 
54.47 ft. as the average distance at which the 50 ft. letters 
were seen. 



23 



Table 2. 
Eesults obtained by the tests made with the 50 ft. letter 



(A) 



56 



(B) 



(C) 



3 


82 


246 


1 


80 


80 


1 


78 


78 


4 


76 


304 


1 


74 


74 


3 


72 


216 


6 


70 
68 


420 


19 


1418 


7 


476 


13 


66 


858 


10 


64 


640 


10 


62 


620 


16 


60 


960 



3554 



15 


58 


870 


13 


56 


728 


18 


54 


972 


14 


52 


728 


17 


50 


850 


77 




4148 


12 


48 


576 


1 


46 


46 


7 


44 


308 


3 


42 


126 


1 


40 


40 


24 




1096 



(A) 



(B) 



(C) 



3 


38 


114 


2 


36 


72 


6 


34 


204 


3 


32 


96 





30 


00 



4 




486 


1 


28 


28 





26 


00 


3 


24 


72 


1 


22 


22 


1 


20 


20 


6 


142 







1 


18 


18 





16 


00 


1 


14 


14 





12 


00 


1 


10 


10 


1 


8 


8 


4 




50 


200 




10894 ft. 



Average distance: 54.5 ft. 



24 



Table 3. 



Results obtained by tests made with the 40 ft. letters 



(A) 



(B) 



(C) 



(A) 



(B) 



(C) 



1 


74 


74 


1 


72 


72 





70 


00 





68 


00 





66 


00 





64 


00 


5 


62 


310 


3 


60 


180 


10 


636 


3 


58 


174 


8 


56 


448 


8 


54 


432 


9 


52 


468 


11 


50 


550 



39 



2072 



21 


48 


1008 


14 


46 


644 


19 


44 


836 


20 


42 


840 


30 


40 


, 1200 


104 




4528 


10 


38 


380 


5 


36 


180 


4 


34 


136 


4 


32 


12S 


6 


30 


ISO 



5 


28 


140 


3 


26 


78 


2 


24 


48 


2 


22 


44 





20 


00 


2 




310 





18 


00 


2 


16 


32 





14 


00 


1 


12 


12 


1 


10 


10 


1 


8 


8 





6 








4 





1 


3 


3 


6 




65 


:00 




8625 ft. 



Average distance: 43.13 ft. 



29 



1004 



25 

Table 4. 
Results obtained by tests made with the 30 ft. letters : 

(A) (B) (C) (A) (B) (C) 

1 60 60 2 18 36 

1 58 58 1 16 16 

1 56 56 2 14 28 

54 00 12 00 

52 00 2 10 20 

50 00 8 00 

2 6 12 

4 00 

13 3 

10 115 

200 6705 ft. 

Average distance 33.5 ft. 



3 




174 


4 


48 


192 


5 


46 


230 


8 


44 


352 


9 


42 


378 


10 


40 


400 


36 




1552 


14 


38 


532 


20 


36 


720 


26 


34 


884 


19 


32 


608 


24 


30 


. 720 


103 




3464 


16 


28 


448 


10 


26 


260 


10 


24 


240 


6 


22 


132 


6 


20 . 


120 


48 




1200 



26 



Table 5. 
Results obtained by making tests with the 20 ft. letters 



(A) 
4 
7 
6 



(B) 
34 
32 

30 



(C) 
136 
224 
180 



17 




540 


19 


28 


532 


21 


26 


546 


31 


24 


744 


35 


22 


770 


38 


20 


760 


144 




3352 



12 
11 

7 

3 

2 

1 

3 

39 
200 



18 
16 
14 
12 
10 



216 

176 

98 

36 

20 

8 

18 

572 
4438 ft. 



Average distance: 22.2 ft. 



Table 6. 
Results obtained by making tests with the 20 ft. dots 



(A) 

1 

2 
5 



(B) 

34 
32 
30 



(C) 
34 
64 

150 



248 



12 


28 


336 


11 


26 


286 


30 


24 


720 


45 


22 


990 


37 


20 


740 


135 




3072 



25 


18 




450 


12 


16 




192 


S 


14 




112 


3 


12 




36 


4 


10 




40 


1 


8 




8 


3 


6 




18 





4 







1 


2 




2 


57 


— 


41'i 


S58 


200 


'8 ft. 


Average 


distance: 


20.9 ft. 





27 

Table 7. 
Results obtained by making tests with the 16 ft. letters 



(A) 


(B) 


(C) 


2 


28 


56 


1 


26 


26 


4 


24 


96 


18 


22 


396 


29 


20 


580 


54 




1154 


59 


18 


1062 


34 


16 


544 


30 


14 


420 


9 


12 


108 


6 


10 


60 


4 


8 


32 


2 


6 


12 


1 


4 


4 


1 


3 


3 


146 




2245 



200 3399 ft. 

Average distance: 16.9 ft. 



Table 8. 
Results obtained by making tests- with the 12 ft. letters 



(A) 


(B) 


(C) 


12 


18 


216 


36 


16 


576 


47 


14 . 


658 


50 


12 


600 


145 


2050 


23 


10 


230 


21 


8 


168 


5 


6 


30 


3 


4 


12 


2 


2 


4 


1 


1 


1 



55 445 

200 2495 ft. 

Average distance: 12.5 ft. 



28 



The combined distance at which the 12 ft. letters could 
be seen was 2,495 ft. This divided by 200, equals 12.48 ft., 
the average distance at which the 12 ft. letters were seen. 

Putting these results in tabular form we have: 

Table 9 



Average distance at which 



50 ft. 


letters 


could be seen 


54.47 ft. 


40 ft. 


> > 


7 7 a 7 7 


43.13 ft 


30 ft. 


> > 


)) }1 ?> 


33.5 ft 


20 ft. 


j » 


> J > > > J 


22.2 ft 


20 ft. 


dots 


> > ) 7 > > 


20.9 ft. 


16 ft. 


letters 


> > > > 7 7 


16.94 ft. 


12 ft. 


? ? 


77 J > > 7 


12.48 ft 



If each one of these different sized letters and the dot 
has the same value in making tests, then the fraction ex- 
pressing the acuteness of vision as shown by the 50 ft. let- 
ter test will be equal in value to the fraction representing 
the acuteness of vision as shown by the tests made by the 
40 ft. letter, the 30 ft. letter, and so on, to the fraction 
representing the acuteness of vision as shown by the 12 ft. 
letter test. In other words, the fractions representing the 
acuteness of vision as shown by making tests with each of 
the different sized letters and the dots will be equal in 
value. 

How nearly this proved to be true with the tests under 
consideration is shown in Table 10. The first fraction was 
obtained by adding the numerators of each of the 200 frac- 
tions representing the acuteness of vision, as shown by each 
test with the 50 ft. letter, and placing this sum over the 
sum of all the denominators, which of course, was, in this 
case, 200x50, because there was a fraction for each of the 
200 pupils tested and the denominator representing the 
acuteness of vision was always 50. 

The second and all the other fractions were obtained 
in exactly the same way, except that the denominators of the 
respective fractions were obtained by multiplying 200 by 
40, 30, 20, etc. 



29 

Table 10 

Fraction's showing the acuteness of vision of 200 pupils 
when tested by the 



10894 



50 ft. 


letters 


10000 

8625 


40 ft. 


) 7 








8000 






6705 


30 ft. 


? J 








6000 






4474 


20 ft. 


yy 








4000 






4186 


20 ft. 


rlotd 






KX\J Lo 


4000 






3387 


16 ft. 

19 ft 


letters 


3200 
2495 



or expressed decimally 1.089 



1.077 



1.118 



1.119 



1.046 



1.056 



1.04 



2400 



Of course, if each of the 200 pnpils had tested np to 
normal with each kind of test the fractions wonld not only 
have been equal in value but each would have been equal to 
one or unity. The decimal parts of the numbers in the 
column to the right show just how much each test is away 
from the normal. Thus the first decimal .089 means that 
tests made with the 50 ft. letters averaged .089 of 50 ft. 
above normal or 4.45 ft. The next decimal .077 means that 
tests made with the 40 ft. letter yield results .077 of 40 ft. 
or 3 ft. above normal, etc. 



30 

If we take the decimal .077 which shows the variation of 
the results obtained by the 40 ft. letter test, as the mean 
variation, then the variation of each of the other decimals 
from this mean would give a result so small that it could 
be neglected in any ordinary tests for acuteness of vision 
with any of the letters or dots. 

These fractions not only show that the amount of vari- 
ation of each kind of test from the mean variation is slight, 
but that all of these variations are uniformly above normal. 

The fact that each one of these tests shows but little 
variation from the normal or from the mean variation does 
not, within itself, necessarily mean that each is equally val- 
uable for making tests of acuteness of vision. Grave errors 
may exist of a plus and a minus nature, but of magnitude 
so nearly equal as not to be disclosed by mere averages. 

The exact location and the exact extent of these varia- 
tions from the assumed normal is shown in tables 2 to 8. 
A glance at these tables shows at once the number of pupils 
(column A), who could see the different tests at different 
distances. These same facts are graphically represented 
in graphs 4, 5, and 6. These graphs not only represent the 
number and extent of the variation from the normal, but 
graph 4 shows the variation of these in the 12 ft., 16 ft., and 
20 ft. letter tests both from the normal and from each other. 
Graph 5 shows the same facts in reference to the 20 ft. let- 
ter test and the 20 ft. dot test. Graph 6 shows these facts 
in reference to tests made with the 30 ft., 40 ft., and 50 ft. 
letter tests. 

In each one of the graphs the line a-b represents 
the assumed distance at which the normal eye could just 
make out the letters or dots. 

The vertical column of numbers at the left represents 
the number of pupils who could see the tests at the differ- 
ent distances. 

The horizontal line of figures beneath the curves in- 
creases by two's, both right and left, beginning at the base 
of the line a-b, and shows the number of feet variation from 
the normal, a-b, made by each group of pupils, indicated by 
the vertical line of figures at the left. The figures to the 
left of the base of line a-b represent the distance above 
normal and the figures to the right, the distance below nor- 
mal. 



31 




Number of feet variation on either side of normal. 
Right side is above normal, left side below normal, 



Graph 4. 



32 




Number of feet variation on either side of -normal 
Right side is above normal, lelt helovr. 



Gkaph 5. 



33 




r-4 «) 



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o c 

<n o 

O r4 

CO ,0 



V +> 

0> r-* 



m 
-*- 

(U +> 

> v-» 
o 

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34 

If all of these seven tests had been of equal value in 
testing normal vision and those above and below normal, 
and, if the curves representing these results had all been 
placed in one figure, then the apexes of each of these curves 
would either have been- on the line a-b or some other line 
parallel to line a-b. 

Furthermore, the curve representing the results obtain- 
ed by testing with the 50 ft. letters would have its apex 
higher than any other curve and the distance between the 
two ends of the curves would be greater than the distance 
between the ends of any of the other curves. Immediately 
under this curve with its apex on the same vertical line 
with the apex of the 50 ft. curve and with its two ends less 
distance apart would come the 40 ft. curve. Then would 
follow the 30 ft., 20 ft., 16 ft. and 12 ft. curves in order, each 
being not so high or wide as its predecessor and the sides of 
each would be parallel with the 50 ft. curve, and, of course, 
with each other, also. 

The curve for the 20 ft. letters and the curve for the 20 
ft. dots, theoretically, should be the same, and, of course, 
would be represented by one and the same curve, if placed 
in the same graph. 

It was found impractical to put all of these curves in 
one graph, so they are shown in three graphs : 4, 5 and 6. 

A glance at these graphs shows at once that no two 
curves are parallel and, consequently, the results of no two 
tests are uniform. As a matter of fact, no two such curves 
will ever be parallel, even if the tests used were of equal 
value as tests, for the personal element, of both the oper- 
ator and the subject, and the influence of environment are 
constantly injecting themselves into and modifying the re- 
sults, consequently, variations of these curves from each 
other are to be expected within certain limits. We can pre- 
scribe these limits, however, and require that results from 
tests obtained by using any size letter and character shall 
come within these limits. 

It would be fair, it seems, in making tests with different 
sized letters and characters to expect that the numbers who 
could see these letters and characters further than 12y 2 % 
of the selected normal distance should be fairly constant. 

The same requirement might be made for the lower limit 
of vision with these same tests. That is, the number un- 



35 

able to see each test without moving nearer to the test than 
12 1 /o% of the selected normal distance should be fairly con- 
stant. 

If this limit were not broad enough then any percentage 
of the normal distance above or below the normal greater 
than 12y 2 % might be taken, as 25%, 37%, or 50%, and we 
could require that the number seeing the different tests 
further than normal by these percentages should be fairly 
constant, and, that the number who could not see the same 
tests without getting nearer to them than the percentages 
of the normal distance indicated, should also, be fairly 
constant. Both of these methods of determining whether a 
test is reliable or not has value. If it is desirable to deter- 
mine how acute the vision of a pupil is who has acute vision, 
then the upper limit method of trying out the tests will be 
of value. If, however, it is desired to know how acute the 
vision of a pupil is who cannot see the test as far away as 
the normal distance, then the lower limit method will be of 
value. But, since most pupils are supposed to have some- 
where near normal vision, it would seem, if the correct 
tests are used, that the number seeing these tests at normal 
and a certain percentage above and below the normal dis- 
tance should be fairly constant, for all the tests. This 
might be called the mean limit of tests for acuteness of 
vision. These methods of determining the relative value 
of testts have been used in connection with the seven dif- 
ferent tests under consideration and the results are shown 
in table 11. 

The (a) portion of this table represents the results ob- 
tained by applying what has been called the " upper limit 
test," for the given percentages above normal, to the re- 
sults obtained from each of the seven tests. 

In (b) is shown the result of applying the "lower limit 
test," with the same percentages, to the results of the same 
tests. 

In (c), is shown the results of applying the "mean limit 
test, ' ' with the same percentages, to the results of the same 
tests. The uniformity of the results shown in (b) by apply- 
ing the "lower limit test" is quite striking in the 12*4% 
line except the numbers under the 16 ft. and the 12 ft. let- 
ters and a close degree of uniformity in all the tests, is 
also seen in the 25%, 37y 2 %, and 50% lines, respectively. 



36 



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37 

According to these figures, either one of the tests ex- 
cept the 12 ft. letter test could be relied upon to detect 
vision, that is less than 50% of normal, or 37%% or 25% 
or even 12y 2 % of normal. Since the detection of poor 
vision, rather than the determination of how many have 
acute vision, above normal, is the chief purpose of testing 
the vision of school children, any of the seven tests under 
consideration except the 12 ft. letter test would be adequate 
for this purpose, especially is this true, if, as is usually the 
case, only those, pupils who have vision less than 25% nor- 
mal are given attention. 

By inspection of the (c) portion of table 11 or that por- 
tion showing the mean variation from the normal, we see 
here, too, a rather close degree of uniformity of results. 
This is especially marked in the figures showing variations 
on both sides of the normal of more than 25%, and, it 
would seem reasonable to expect that any vision test that 
makes any pretension to reliability should show similar re- 
sults when this test is applied. 

If we now give our attention to the (a) portion of table 
11, we see here, too, a rather close degree of uniformity in 
all the tests for the upper limit of vision for all the per- 
centages taken above normal. Since the application of all 
of these tests to the tests under consideration give fairly 
uniform results, it is reasonable, it seems, to conclude that 
the results in general will be about as accurate with one 
test as with another. Exceptions, however, will have to be 
made with the 12 ft. letter tests, although the figures in the 
tables would seem to indicate that this test is generally 
about as good as any of the other tests. This exception 
will have to be made in spite of these figures, because in at 
least two cases of undoubted nearsightedness, the pupils 
could not see the larger letters at anything like the normal 
distance, but they could see the 12 ft. letters at about nor- 
mal. 

The variation of results of certain tests from the results 
of other tests as shown in table 11 demands some attention. 

In the (a) portion of the table it is noted that the num- 
ber seeing the 20 ft. dots beyond the normal distance by the 
different given percentages is smaller in every case than 
with any of the other tests except the 16 ft. letter. From 
the data obtained from these tests it is not possible to as- 






38 

sign a reason why the 16 ft. letters were not seen as far 
proportionately above the normal as were the twenty ft. 
letters or any of the other letters, but it is believed that the 
failure to see the 20 ft. dots as far as the letters, can be 
accounted for in this way. In deciding what a letter is, 
the element of intelligence as well as the ability to see 
enters in as a determining factor much oftener than is the 
case with deciding wiiether the dot is seen or not. 

In seeing the dot only two things can enter into the mind 
on which a decision is to be made, and these two things are, 
is the dot there, or is it not there, or does the dot make a 
sensation on the retina or does it not. The decision that is 
made will depend almost exclusively upon pure retinal sen- 
sation. While in the case of seeing the letter there can be 
no doubt that the. letter is seen, that a retinal impression is 
made, but in deciding what the letter is that is making this 
particular impression, often, undoubtedly, involves a com- 
plicated mental operation, in which the general shape and 
appearance of the letter play a very important part. 
Hence, one must expect fewer pupils to see the 20 ft. dot 
at distances considerably above normal than will see the 
same sized letters or letters of any size at proportional dis- 
tances. 

This expectation is borne out by the figures in (b), table 
11. Here it is seen that the dot shows up more pupils with 
defective vision, on the average than any of the letter tests, 
at the percentages below normal given, except the 12 ft. 
letter. 

The figures in (c) under the 20 ft. dot column also show 
that the letters of all sizes above the 16 ft. letters can be 
seen better than the 20 ft. dot at the same relative distances. 
Take, for example, the 12y 2 % variation on either side of 
normal, there were only 90 pupils who could not read the 50 
ft. letters, while there were 117 who could not make out 
the dot at the same relative distance from normal. The 
fact that the vision of the 200 pupils tested averaged 
above normal and that more pupils saw the 20 ft. dots at 
the average distance above normal than for any of the other 
tests, and, since the number found with defective vision 
was unusually small, but the dot test showed more than 
any, one would be inclined to the belief that the dot is the 
best of any of the tests used. One would be justified in 



39 

coming to k this conclusion, not only because it tests vision, 
and vision only, and the results are more in harmony with 
what other investigators have found out about the number 
of children who have defective vision, but, also, because of 
the simplicity of the test and the fact that it can be used to 
test little children, illiterates or literates with equal ease 
and accuracy. Further evidence that the dot is a good test 
is shown by the fact that there was not a single case of poor 
vision detected among the 200 pupils by any of the other 
tests that was not also detected by the dot test. This was 
also true with the tests made with the 16 ft. and the 12 ft. 
letter, except in the two cases mentioned above. This 
shows undoubtedly that for certain defects of the eye the 
12 ft. letters are not reliable. The 16 ft. letters were found 
to be reliable for the detection of all cases of poor vision 
that would need attention and which were detected by the 
other tests. 

The results of these tests clearly justify one in drawing 
the following conclusions : 

1. The "illiterate E" as now constructed is practically 
useless as a test of the acuteness of vision. If it is to be 
used as a test when constructed of the size of the 16 ft. let- 
ter, then the distance at which it should be placed from the 
one being tested should be, not 16 ft., but 26 ft. Or, if the 
16 ft. distance is to be maintained then the size of the letter 
must be reduced to 16/26 of its present size. 

2. The 20 ft. dot test is thoroughly reliable for testing- 
poor vision, normal vision, or acute vision. None of the 200 
pupils tested seemed to have any optical trouble — myopia, 
hyperopia, astigmatism or any other optical defect — that 
was not detected by this test as well or better than by any 
other test. 

3. The 16 ft. letter test is reliable for all defects of suffi- 
cient gravity to justify the teacher in recommending the 
pupil to go to an oculist. 

4. The 12 ft. letter test will detect most of the graver 
defects of vision, but not all, therefore, it is not to be relied 
upon. 

5. The eyes of 150 of the 200 pupils, subjected to these 
tests were tested, one eye at a time, a few weeks before. 



40 

Every pupil, with four exceptions, who had vision 25% or 
more below normal, as shown by this one-eye-at-a-time test, 
could with two eyes make a better showing. Not only was 
this true of pupils having poor vision, but it was equally 
true of all other pupils. This can be taken as an indication, 
not only, that binocular vision is better than monocular 
vision, but it accounts for the fact that the pupils in these 
tests averaged above normal in vision. 



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